Bourbaki

Definition 2

Tag 03AM, permanent. Cite it as [Bourbaki, Tag 03AM].

Théories spectrales, chapter V, § 2. Représentations des groupes localement compacts

One says that the unitary representation of G in the space Lπ‾2(G)L^2_{\overline{\pi}}(G) thus defined is the unitary representation of G induced by the representation π\pi of H relative to κ\kappa. It is denoted by IndHG(π,κ)^G_H(\pi , \kappa ), or simply IndHG(π)^G_H(\pi ).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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Cites

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Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.